To compute the energy spectra in Fig. REF  from our simulations, we select the macro-particles lying in the neighborhood of the spacecraft trajectory. In particular, we use a range of \(\pm 4\)  cells (equal to \(\approx \pm \) 0.06R) in all directions in order to minimize the particle noise and mimic the effect of particle precipitation on the instruments in an acquisition time \(\delta t\) . Moreover, we assume that the field of view of the instruments spans the whole \(4\pi \)  solid angle in an acquisition time \(\delta t\) . Although this assumption is usually partially verified by the instruments, the main features of the spectra in Fig. REF  are expected to hold also in the case of limited field of view.
To ease the comparison with in situ observations, the spectra in Fig. REF a-b have the same energy range and resolution of the Mariner10/PLS instrument [1]} and those in Fig. REF e-f of the BepiColombo/MEA1 [2]} instrument operating in solar-wind mode during the flyby. Moreover, in Fig. REF  we report the bow shock and magnetopause crossing times obtained by the two spacecraft in situ at Mercury as discussed in [3]} (panels a-d) for Mariner10 and in [4]} for BepiColombo (panels e-h).
In the following, we discuss these two spacecraft flybys modeling results separately.
